US6909221B2 - Piezoelectric on semiconductor-on-insulator microelectromechanical resonators - Google Patents

Abstract

A piezoelectric resonator is disclosed. In one embodiment the piezoelectric resonator includes a resonating member having a bi-directionally adjustable resonance frequency, the resonating member including a semiconductor material of a semiconductor-on-insulator wafer, the semiconductor-on-insulator wafer including an oxide layer adjacent to the semiconductor material and a handle layer adjacent to the oxide layer, the oxide layer disposed between the handle layer and the semiconductor material, and electrode, and a piezoelectric material disposed between the semiconductor material and the electrode, and a capacitor created by the semiconductor material and the handle layer separated by an air gap formed out of the oxide layer, wherein the capacitor is configured to receive a direct current voltage that adjusts the resonance frequency of the resonating member.

Description

CROSS-REFERENCE TO RELATED APPLICATION

This application claims the benefit of U.S. Provisional Application No. 60/400,030, filed Aug. 1, 2002, which is entirely incorporated herein by reference.

This application is related to copending U.S. Utility patent application entitled “Capacitive Resonators and Methods of Fabrication,” Ser. No. 10/632,176, filed on the same date.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

The U.S. government has a paid-up license in this invention and the right in limited circumstances to require the patent owner to license others on reasonable terms as provided for by the terms of Contract No. DAAH01-01-1-R004 awarded by the U.S. Army.

TECHNICAL FIELD

The present invention is generally related to MEMS (micro-electro-mechanical systems) technology, and, more particularly, is related to piezoelectric resonators.

BACKGROUND OF THE INVENTION

Advanced consumer electronics such as miniature radios and wristwatch cellular phones pose severe limitations on the size and cost of frequency selective units contained therein. MEMS (micro-electro-mechanical systems) resonators are receiving increased attention as building blocks for integrated filters and frequency references to replace bulky, off-chip ceramic and SAW (surface acoustic wave) devices, among others. Small size, low power consumption and ease of integration with microelectronic circuits constitute the major advantages of MEMS resonators.

Several all-silicon resonators with capacitive transduction mechanisms are known, revealing high mechanical quality factors (Q) and optimal performance in the IF (intermediate frequency) and VHF (very high frequency) range. However to reduce the motional resistance of such capacitive resonators for higher frequency applications, gap spacing on the order of nanometer dimensions are often required, which can complicate the fabrication process for these devices.

Piezoelectric Film Bulk Acoustic Resonators (FBAR), characterized by a lower motional resistance than their capacitive counterparts, have proven to be suitable for UHF (Ultra-high frequency) applications. However, FBAR resonators generally have low quality factors and no electrostatic fine-tuning capabilities. Further, fabrication methods for these devices are limited practically in their ability to create thick and/or uniform mechanical layers due in part to the long processing times associated with fabrication of thick substrates.

Thus, a need exists in the industry to address the aforementioned and/or other deficiencies and/or inadequacies.

SUMMARY OF THE INVENTION

Embodiments of the present invention provide piezoelectric resonators.

Briefly described, one embodiment of the piezoelectric resonator, among others, includes a resonating member having a bi-directionally adjustable resonance frequency, the resonating member including a semiconductor material of a semiconductor-on-insulator wafer, the semiconductor-on-insulator wafer including an oxide layer adjacent to the semiconductor material and a handle layer adjacent to the oxide layer, the oxide layer disposed between the handle layer and the semiconductor material, an electrode, and a piezoelectric material disposed between the semiconductor material and the electrode, and a capacitor created by the semiconductor material and the handle layer separated by an air gap formed out of the oxide layer, wherein the capacitor is configured to receive a direct current voltage that adjusts the resonance frequency of the resonating member.

Other systems, methods, features, and advantages of the present invention will be or become apparent to one with skill in the art upon examination of the following drawings and detailed description. It is intended that all such additional systems, methods, features, and advantages be included within this description, be within the scope of the present invention, and be protected by the accompanying claims.

BRIEF DESCRIPTION OF THE DRAWINGS

Many aspects of the invention can be better understood with reference to the following drawings. The components in the drawings are not necessarily to scale, emphasis instead being placed upon clearly illustrating the principles of the present invention. Moreover, in the drawings, like reference numerals designate corresponding parts throughout the several views.

FIG. 1 is a schematic diagram that illustrates one exemplary implementation for the embodiments of the invention.

FIGS. 2A-2C are schematic diagrams that illustrate several piezoelectric beam resonator embodiments.

FIG. 3 is a schematic diagram that illustrates a piezoelectric block resonator embodiment.

FIG. 4A is a flow diagram that illustrates one method embodiment for fabricating the piezo electric resonator embodiments shown inFIGS. 2A-3.

FIGS. 4B-4E are schematic diagrams that illustrate the method shown in FIG.4A.

FIG. 5 is a schematic diagram that illustrates an equivalent electrical circuit for the piezoelectric resonator embodiments ofFIGS. 2A-3.

FIG. 6 is a graph that illustrates resonance frequency as a function of direct current (DC) voltage for the piezoelectric resonator embodiments ofFIGS. 2A-3.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

Embodiments of piezoelectric resonators and methods for fabricating the same are disclosed. In general, the piezoelectric resonator embodiments include voltage tunable, piezoelectrically-transduced, high-mechanical Q (Quality Factor) semiconductor resonators (or resonating element) derived at least in part from semiconductor-on-insulator (SOI) substrates. The embodiments of the invention include substantially all semiconductor materials for the resonating element, such as germanium, silicon, among others. Further, the embodiments of the invention include substantially all semiconductor materials in a variety of crystal alignments or configurations, including single crystal structures, poly structures, amorphous structures, among others. Q can generally be described as a measure of energy stored in a system divided by the energy dissipated in the system. Q can be characterized in terms of frequency response of a resonator, such as the ratio of the center frequency (f₀) to the 3-dB (decibel) bandwidth of the resonator device. An active piezoelectric thin-film material, such as zinc-oxide (ZnO), aluminum nitride (AlN), lead zirconate titanate (PZT), etc., is disposed between an electrode (e.g., comprised of a metal such as aluminum) and a low resistivity silicon or other semiconductor material. One mechanism for choosing an appropriate piezoelectric material can be based on selecting a higher product value of the combination of the material's Young's modulus and piezoelectric coefficient. The thin piezoelectric film provides for high electromechanical coupling and/or provides for small equivalent motional resistance (e.g., equivalent resistance of the device in the electrical domain), hence reducing noise problems and enhancing filter designability. In one embodiment, the resonating element can be substantially made out of single crystal silicon (SCS), which has a higher inherent mechanical Q than bulk piezoelectrics. Functions of actuation and sensing are preferably achieved by piezoelectric mechanisms. In other words, the piezoelectric material or thin film functions as the transduction element of the device.

Through the use of the SOI substrate, piezoelectric actuation mechanisms can be combined with electrostatic fine-tuning for the center frequency of a given resonator. For example, by applying a DC voltage to a capacitor located between a handle layer of the SOI substrate and the resonator body (e.g., SCS device layer) it is possible to introduce “electrical stiffness” through the action of the capacitance, hence modifying the equivalent stiffness of the beam. In other words, when an electrical field is applied, it is equivalent to applying a defined force that causes a deflection of the resonating element, which in turn causes a change in the internal stress or stiffness of the resonating element.

The following description will guide the reader through several embodiments of a piezoelectric resonator, a method of fabricating the same, and provide performance characteristics of such devices.

The preferred embodiments of the invention may, however, be embodied in many different forms and should not be construed as limited to the embodiments set forth herein; rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the invention to those having ordinary skill in the art. For example, although the embodiments of the invention can be used with substantially any semiconductor substrate and/or piezoelectric material, the preferred embodiments of the invention will be described using an SCS resonating element and a ZnO thin film for the piezoelectric material, with the understanding that other semiconductor materials in different crystal alignments or structures and/or different piezoelectric material are also included within the scope of the invention.

FIG. 1 is a schematic diagram that illustrates one exemplary implementation for the embodiments of the invention. Select receiver components of acommunication device120 are shown, with the understanding that transmitter components can also benefit from the embodiments of the invention. Thecommunication device120 can include a portable transceiver, such as a cellular phone, among other devices. Thecommunication device120 includes anantenna102, piezoelectric resonator devices100a-100cconfigured as frequency selective filters, low-noise amplifiers106 and114,mixers108 and116, voltage-controlledoscillators110 and118, and a frequency referencepiezoelectric resonator device100d.All components shown except for resonator devices100a-100dare known, and thus further explanation is omitted for brevity. The use of piezoelectric resonators100a-100dcan result in a reduction in the number of components in thecommunication device120. Piezoelectric resonators100a-100dare very selective at high frequencies, thus substantially obviating the need for pre-amplifler selection and other frequency transformation and/or amplification devices that operate to provide signal processing at frequencies that current devices most efficiently operate under. The piezoelectric resonator devices of the preferred embodiments possess high quality factors at high frequencies, enabling frequency selection with substantially fewer components.

FIGS. 2A-2C are schematic diagrams that illustrate several piezoelectric beam resonator embodiments.FIG. 2A is a schematic diagram of a first embodiment configured as a clamped-clampedresonator beam200a. The clamped-clampedresonator beam200aincludes ahandle layer202, anoxide layer204, adevice layer206, apiezoelectric layer208, adrive electrode210, and asense electrode212 a The “clamped”regions201 and203 correspond to the location where the SOI substrate is secured to theunderlying handle layer202, which in turn can be secured to a printed circuit board, among other devices. In some embodiments, theunderlying handle layer202 is the substrate in an integrated circuit, to which the SOI portion is secured. The “beam”region205, having a length “L,” spans between the two clampedregions201 and203, and includes the portion of thepiezoelectric resonator200athat is free to vibrate. Thedevice layer206 and theoxide layer204 collectively represent the SOI substrate. Some exemplary thicknesses of the device layer206 (e.g., Ts) can range from approximately 4.0-5.0 microns, although different thickness ranges are possible (e.g., 0.2 microns-30 microns). Some exemplary thicknesses of theoxide layer204 range from approximately 1.0-5 microns. Thehandle layer202 provides mechanical support for the clamped-clampedbeam resonator200a. Thepiezoelectric layer208 is disposed in precise locations between theelectrodes210 and212aand thedevice layer206. Thepiezoelectric layer208 can have a thickness of 0.2 microns-0.3 microns, as one example range. Thedevice layer206 can be a low resistivity SCS substrate, with higher quality silicon (e.g., zero or substantially zero defects) situated in the upper region of thedevice layer206. Theelectrodes210 and212acan be comprised of aluminum, among other metals, and example thicknesses include a range of 0.1-0.2 microns. The absence of a bottom metal electrode (e.g., a bottom electrode is conventionally used for piezoelectric devices) reduces the number of stacked layers, which could ultimately affect the mechanical Q of the resonator.

In operation, an alternating current (AC) voltage (source not shown) can be applied at thedrive electrode210 according to well-known mechanisms. Responsively, thepiezoelectric layer208 produces a distributed moment, which causes thebeam205 to deflect in the “z” direction (e.g., out-of-plane deflections). The deflection is sensed at thesense electrode212aas a result of the piezoelectric effect.

Well-known admittance models of a doubly-clamped piezoelectric beam resonator can be used with modification to model the behavior of the clamped-clampedresonator beam200a. The electromechanical coupling coefficients at thedrive electrode210, η_in, in and at thesense electrode212a, η_outof the clamped-clampedresonator beam200aare expressed by:$\begin{array}{cc}{\eta }_{in}=\frac{d_{31}{E}_p{T}_s}{2}{\int }_0^L{W}_i^{″}\left(x\right)\Phi \left(x\right)dx& \left(\mathrm{Eq}.1\right)\\ {\eta }_{\mathrm{out}}=-\frac{d_{31}{E}_p{T}_s}{2}{\int }_0^L{\mathrm{<figure-callout\; label="W"\; filenames="US06909221-20050621-D00010.png"\; state="\{\{state\}\}">W</figure-callout>}}_0\left(x\right){\Phi }^{″}\left(x\right)dx& \left(\mathrm{Eq}.2\right)\end{array}$
where d₃₁is the transverse piezoelectric coefficient, E_pis the modulus of elasticity of ZnO, and Φ(x) is the function describing the mode shape of the clamped-clampedresonator beam200a. Note that slightly different equations for piezoelectric resonator blocks apply, as would be understood by those having ordinary skill in the art. Ts is the height of thedevice layer206. The equivalent motional resistance of the resonating element (e.g., the beam205) depends on the squared inverse of the electromechanical coupling. Therefore the values of η_inand η_outare preferably maximized to achieve low values of the motional resistance. The maximum value of the two integrals in Eqs. 1 and 2 occurs for electrode edges placed at inflection points of the beam mode shape. In one embodiment, the inflection points coincide with 22.4% and 77.6% of the beam length. Therefore the final input to output admittance, Y_oi, of an SCS resonator (i.e., a resonator that includes a device layer comprised of SCS) with piezoelectric transduction becomes:$\begin{array}{cc}{Y}_{oi}=\frac{{\left(2.49·d_{31}{E}_p{T}_s\frac{W}{L}\right)}^{2}s}{M_1{s}^2+\frac{M_1{\omega }_n}{Q}s+K_1}& \left(\mathrm{Eq}.3\right)\end{array}$
where M₁and K₁are first mode equivalent mass and stiffness of the micromechanical resonator, ω_nis the natural resonance frequency of the beam, s is the Laplace variable, and W is the width of theelectrodes210 and212a.If the thickness of thepiezoelectric layer208 is negligible compared to the height, Ts, of the silicon material of the resonator body, the resonance frequency can be approximately expressed by the equation for a beam with isotropic properties:$\begin{array}{cc}{\mathrm{<figure-callout\; label="f"\; filenames="US06909221-20050621-D00010.png"\; state="\{\{state\}\}">f</figure-callout>}}_0=1.03\frac{T_s}{L^2}\sqrt{\frac{E_s}{{\rho }_s}}& \left(\mathrm{Eq}.4\right)\end{array}$
where E_sand ρ_sare respectively the modulus of elasticity and the density of silicon.

FIG. 2B is a schematic diagram of a second embodiment configured as a clamped-clampedresonator beam200bwith thepiezoelectric layer208 etched away. Layers similar to202-206 andelectrodes210 and212aofFIG. 2A are the same as shown in FIG.2B and thus are not discussed here for clarity. Thepiezoelectric layer208 is etched in approximately the middle span of thebeam205 to reduce the effective covering of thebeam205 by thepiezoelectric layer208, thus exposing a surface of thedevice layer206. Reducing the effective covering of thebeam205 by thepiezoelectric layer208 can enhance the mechanical Q of thepiezoelectric beam resonator200b(e.g., experimentally proven to at least double the mechanical Q when compared to the embodiment illustrated in FIG.2A).

FIG. 2C is a schematic diagram of a third embodiment configured as a clamped-clampedresonator beam200cwith asensing electrode212bthat extends further along thebeam205 than thesensing electrode212aofFIGS. 2A-2B. The extending of thesensing electrode212bcovers the area where the strains have the same sign, thus maximizing the sensed strains and providing for improved sensing capability. Thesensing electrode212bextends over the middle span of thebeam205, with the edges located at the inflection points of the beam mode shape. Thesensing electrode212bmay cover approximately twice the area covered by thesensing electrode212a.

FIG. 3 is a schematic diagram that illustrates another embodiment in the form of apiezoelectric block resonator300. Thepiezoelectric block resonator300 includes ahandle layer302, anoxide layer304, adevice layer306, apiezoelectric layer308, adrive electrode310, and asense electrode312. As shown, thepiezoelectric block resonator300 has a structural configuration that includes amain block305 centrally supported by self-alignedsmall tether regions301 and303. The resonating element can be comprised of SCS, which has a high inherent mechanical quality factor and stress-free properties. Thepiezoelectric layer308 can be comprised of a thin ZnO film that can be sputtered on the top surface of thedevice layer306. The ZnO film functions as an insulator between theelectrodes310,312 and thedevice layer306. Thepiezoelectric layer308 enables piezoelectric sense and actuation. Thedrive electrode310 and thesense electrode312 can be comprised of aluminum. Thedrive electrode310 andsense electrode312 are configured in a manner to be excited longitudinally (e.g., in-plane displacement), providing for higher frequencies and high order modes. Theoxide layer304 is absent underneath all areas of thepiezoelectric block resonator300 except for the regions substantially under the drive and sense electrode (or pads)310 and312 at the end of thetethers301 and303. The absence of theoxide layer304 under these regions enables high frequency, in-plane movement characteristic of thepiezoelectric block resonator300 of the preferred embodiments.

Pure and quasi-length extensional modes can be observed forpiezoelectric block resonators300 of varying lengths. The frequencies of the pure extensional modes for thepiezoelectric block resonator300 are given by equation (5):$\begin{array}{cc}{\omega }_n=\frac{\left(2n-1\right)\pi }{2l}\sqrt{\frac{E}{{\rho }_s}}n\mathrm{is}\mathrm{mode}\mathrm{number}\left(n=1,2,3,\dots \right)& \left(\mathrm{Eq}.5\right)\end{array}$
The use of higher order modes of vibration for thepiezoelectric block resonator300 enables high frequency operation because the natural frequency grows as (2n−1). Further, the use of a block-type structure results in a structure whereby the dimensions of the structure can be kept in a range that can be easily fabricated using optical lithography. Equivalent motional resistance is reduced for this structure, due in part to the high electromechanical coupling factor attributed by piezoelectric transduction. Thus, the signal-to-noise ratio is improved over other transduction devices, such as capacitive devices.

FIG. 4A is a flow diagram that illustrates one method for fabricating the piezoelectric resonator embodiments shown inFIGS. 2A-3. Note that the method is based on one implementation, and that alternate implementations are included within the scope of the preferred embodiments of the invention such that steps can be omitted, added to, and/or executed out of order from that shown or discussed, as would be understood by those reasonably skilled in the art of the present invention.FIGS. 4B-4E are schematic diagrams that are used in cooperation withFIG. 4A to illustrate some of the structural changes that occur during the fabrication method. In general, the fabrication method of the preferred embodiments includes a simple three-mask process that can be used as a fabrication technology for SCS (or other) microelectromechanical resonators used for piezoelectric transduction. Structures similar to or the same as those shown for the clamped-clampedresonator beam200bofFIG. 2B are used as a non-limiting example, with the understanding that the process applies similarly to the other embodiments shown inFIGS. 2B,2C and3. As shown inFIG. 4B,structure400acomprises ahandle layer202 adjacent to a semiconductor-on-insulator (SOI) substrate. The SOI substrate comprises anoxide layer204 and adevice layer206. Theoxide layer204, as described above, is disposed between thehandle layer202 and thedevice layer206.

Thedevice layer206 can be comprised of a SCS structure. SCS structures can be made in a wide variety of defined thicknesses. Athicker device layer206 translates to a wider frequency range. In contrast, conventional systems may use SiO₂, which is typically deposited and thus has larger constraints to increasing thickness since the barrier to oxidation increases as the thickness increases.

Referring toFIGS. 4A and 4B,step401 includesetching trenches420a,420bin thedevice layer206 of the SOI substrate. This etching step defines the resonator body. In one embodiment, thetrenches420a,420bare etched to theoxide layer204, and have a width of approximately 4 micro-meters (μm). The etching can be performed using reactive ion etching (RIE), such as regular RIE (e.g., for depths of 4-5 microns), or deep reactive ion etching (DRIE) (e.g., for depths greater than 10 microns) using the Bosch process, among other processes. The height of the silicon layer (device layer206) of the beam205 (FIG.2A), for example Ts ofFIG. 2A, is defined by the thickness of thedevice layer206. As one example, thedevice layer206 of the selected SOI can be p-type, with low resistivity, a <100> orientation, and with a nominal thickness of 4±1 μm. Further, theoxide layer204 can be 1 μm thick and thehandle layer202 can be n-type, having a <100> orientation with a nominal thickness of 400 μm. The choice of an n-type substrate does not necessarily depend on particular design parameters, but primarily on substrate availability.

Referring toFIGS. 4A and 4C,step403 includes etching theoxide layer204 of the SOI substrate to formstructure400b. In other words, a cavity is opened underneath thedevice layer206. For example, the cavity can be created by isotropic etching of theoxide layer204 in hydro-flouric acid (HF) solution having a molar concentration of approximately 49%, among other solutions and/or molar concentrations. This etching step provides for a small gap (e.g., approximately 1 μm) that can be used for capacitive fine-tuning of the beam center frequency.

Referring toFIGS. 4A and 4D,step405 includes applying a piezoelectric material to the SOI substrate to formstructure400c. For example, a piezoelectric material, such as ZnO, can be sputter-deposited on the SOI substrate to form apiezoelectric layer208. Other options for applying include high-temperature growth of the ZnO, among others. ZnO is an acceptable choice for the piezoelectric material because of its well-known process of fabrication and ease of integration with current microelectronics. In fact, no high temperature processes are involved in all the fabrication steps described herein. Thus, integration with actual CMOS (complementary-metal-oxide-silicon) technology could be simply implemented as a post-CMOS process. Exemplary deposition parameters can include a temperature of 250° C. for the SOI substrate, a pressure of 6 mTorr, an Ar to O₂mix ratio of 0.5, and a power level of 300 W.

Referring again toFIGS. 4A and 4D,step407 includes the patterning of the piezoelectric material. For example, ZnO can be patterned by wet etching using ammonium chloride (NH₄Cl), 5% at 55° C. NH₄Cl is a good choice in that it has a very slow etch rate (50 Å/s) and enables the definition of small features, avoiding severe lateral undercutting. Note that for embodiments where the piezoelectric material is not etched (e.g., the piezoelectric resonator embodiments shown in FIGS.2A and2C),step407 can be omitted. Further, in some embodiments, an additional step can include providing an adhesion layer (e.g., a metal) to improve the adhesion of the piezoelectric material.

Referring toFIGS. 4A and 4E,step409 includes providing an electrode410 (e.g., such aselectrodes210 and/or212a,bofFIG. 2) to the piezoelectric material (i.e., piezoelectric layer208). In one embodiment, theelectrode410 is defined by a third mask using lift-off (e.g., lifting off portions not needed using a sacrificial layer). For example, 1,000 Å of aluminum can be deposited by electron-beam evaporation. Keeping the thickness of the ZnO and Al layers as low as possible can provide for maximum mechanical Q, in addition to avoiding or mitigating any detrimental effects due to stacked layers of different materials.

Piezoelectric resonators fabricated using the above-described method were tested in a custom-built vacuum chamber capable of pressures as low as 10 μTorr.

A low-noise JFET (junction field-effect transistor) source-follower with a gain stage was used to interface with the piezoelectric resonators of the preferred embodiments. The sensing interface was built on a printed circuit board (PCB) using surface mount components. The piezoelectric resonator was mounted on the board and wire-bonded. The frequency spectra of the resonators were attained by using a network analyzer.

Table 1 below lists the frequency responses taken from the network analyzer for a 100 μm long, 20 μm wide clamped-clamped beam and a 200 μm long, 20 μm wide clamped-clamped beam fabricated using the above method and illustrated by the embodiment shown in FIG.2B. The peak frequency values for 1^st, 3^rd, 5^th, and/or 6^thresonance modes were determined, the peak values representing the mechanical resonance of the piezoelectric resonator. One purpose for evaluating for higher resonance modes (e.g., harmonics) is to evaluate the quality factor at these higher frequencies.

TABLE 1
(beam-style)

Dimensions

Q

length	width					(Quality
(μm)	(μm)	F0-1st	F0-3rd	F0-5th	F0-6th	Factor)

100	20	1.72 MHz				6200
200	20	.721 MHz				5400
200	20		3.29 MHz			5300
200	20			4.87 MHz		3000
200	20				6.70 MHz	2400

As shown in the first row entry of Table 1, the resonator having a length of 100 μm and a width of 20 μm has a center frequency of 1.72 MHz and shows a quality factor of 6,200 at a pressure of approximately 50 mTorr. Piezoelectric resonators with different configurations (e.g., the embodiment shown inFIG. 2A) were tested and showed Qs about two times smaller, in the order of 3,000. Such high values of the quality factor confirm that the choice of SCV as the resonating material is an optimal choice. Further, actuation voltages as low as 700 μV (e.g., the minimum value enabled by the network analyzer) can excite the piezoelectric resonators, which can show a dynamic range of approximately 45 dB or better.

The piezoelectric resonators of the preferred embodiments can be operated in higher order modes, hence enabling higher frequencies. The placement of the electrodes can be optimized for operation in the fundamental mode. Some high order modes have inflection points within the electrode region, which decimates the charge build-up from the piezoelectric material. Therefore, some of the high order modes cannot be sensed. With the increased degrees of freedom, there are additional high order modes. The frequency responses of a 200 μm long beam in its 1^st-6^thmode are also shown in Table 1. A Q of 5,400 at 0.721 MHz was shown at the first resonance mode. A Q of 5,300 at 3.29 MHz was measured for the third resonance mode, with no substantial decrease from the first mode quality factor. The Qs for the fifth and sixth modes, respectively at 4.87 MHz and 6.7 MHz, are approximately halved: a Q of 3,000 was recorded for the fifth mode and a Q of 2,400 for the sixth mode. Thus, as shown in Table 1, by exciting the harmonics, high quality factors (e.g., over 1000) were achieved.

Table 2 below lists the first and second order frequency responses taken from the network analyzer for piezoelectric block resonators, similar to or the same as the embodiment shown in FIG.3. In particular, piezoelectric block resonators having a thickness of 4-5 μm and dimensions of (a) 480 μm length×120 μm width, (b) 120 μm length×40 μm width, and (c) 240 μn length×20 μm width were tested in an approximately 50 mTorr vacuum, similar to the test arrangement described in association with Table 1. Note that for piezoelectric block resonators of the preferred embodiments, frequency response is not a function of block thickness. Such a feature substantially alleviates the need for uniform substrate thickness.

TABLE 2
(block-style)

Dimensions

	length	width
	(μm)	(μm)	F0-1stand 2nd	Q (Quality Factor)

	480	120	66.6 MHz	5500
	480	120	195 MHz	4700
	120	40	35 MHz	4500
	120	40	104 MHz	4500
	240	20	16.9 MHz	11,600

As shown, the 480 μm×120 μm piezoelectric block resonators demonstrated high-Q resonant peaks at 66.6 MHz (with Q of 5,500) and 195 MHz (with Q of 4,700) in a 50 mTorr vacuum. These peaks correspond to two quasi-length-extensional mode shapes of the 480×120 μm block. It should be noted that these quasi-extensional modes cannot be calculated using equation (5) above as they show substantial thickness modulation. When testing operation in air, the Q of the 67 MHz peak was reduced only by a factor of 1.25 compared to its Q in vacuum. Higher order modes were also observed in testing.

For the 120 μm×40 μm block resonator, the first and second extensional modes were measured at 35 MHz and 104 MHz (with Q of 4,500), which is in good agreement with theoretical values calculated using equation (5). The highest Q measured for the block resonators was 11,600, which has been measured for the first extensional mode of a 240 μm×20 μm block at 17 MHz. ANSYS simulations were also performed that verified the observed resonant peaks for the data shown in Table 1 and Table 2.

FIG. 5 shows acircuit arrangement500 including anequivalent circuit502 for modeling the resonance behavior of a piezoelectric beam and block resonators of the preferred embodiments and a trans-resistance amplifier circuit504 that can be used in conjunction with theequivalent circuit502. As shown, theequivalent circuit502 includes an input voltage (V_in) which corresponds to the potential at a drive electrode. Vin can be, for example, 1 millivolts (mV) to 100 mV. Theequivalent circuit502 includes parasitic capacitance (C_p) associated with the capacitance between the bonding pads and ground. The feed-through capacitance, C_FTcorresponds to the capacitance between the input and output port (e.g., the distance between the electrodes located on thebeam205 of FIG.2A). The body of the resonator (e.g., resonating element) can be modeled with the series capacitor (C_m), resistor (R_m), and inductor (L_m). For example, the frequency response of the mechanical resonator is determined by:
f=1/[(2π(LC)^1/2]  (Eq. 6)
The assumption made for theequivalent circuit502 is that the sense electrode is at virtual ground, enabling modeling as a unilateral device. The output current (i_out) is provided to a high impedance device, such as the operational amplifier of the trans-resistance amplifier circuit504, where a voltage drop is created across the resistor, R, of the trans-resistance amplifier504. The value of the voltage is implementation-dependent. The larger the value of R of the trans-resistance amplifier504 and/or the smaller the output current, the larger the output voltage (V_out).

Electro-static fine-tuning is enabled by the structure of the piezoelectric resonators of the preferred embodiments. In general, tuning is performed by the application of a DC voltage across a capacitor located between the device layer and the handle layer of a piezoelectric resonator, such as the “beam” style piezoelectric resonator. The application of the DC voltage creates a negative mechanical stiffness, which tends to decrease the resonance frequency with the application of increasing DC voltage, thus providing a tuning effect. Another mechanism to provide tuning is to etch out another electrode adjacent to the main “beam” portion of a block-type resonator. The in-plane movement with respect to the adjacent electrode creates a variation in capacitance. Thus, the piezoelectric block resonators provide for voltage-tunable functionality.

FIG. 6 shows agraph600 that provides a comparison between the measured (curve652) and the theoretical (curve650) frequency-tuning characteristic for a 200 μm long beam-style, 719 kHz resonator. The data for thisgraph600 is determined by changing the DC voltage applied to a capacitor between the handle layer of the SOI wafer or substrate and the device layer of a piezoelectric resonator from 0 to 20V. Axis646 provides an indication of resonance frequency, andaxis648 provides an indication of DC voltage. Shown is an electrostatic tuning range of 6 kHz. The tunable frequency characteristics are uniquely related to the fabrication methodology described in association with FIG.4. This fabrication methodology enables the combination of piezoelectric transduction mechanisms with electrostatic tuning, the latter of which was generally considered a sole prerogative of capacitive resonators. Uncertainty on the exact extension of the etched area underneath the beam (e.g., of thedevice layer206,FIG. 2A, for example) could account for the small mismatch between the theoretical andexperimental curves650 and652, respectively.

It should be emphasized that the above-described embodiments of the present invention, particularly, any “preferred” embodiments, are merely possible examples of implementations, merely set forth for a clear understanding of the principles of the invention. Many variations and modifications may be made to the above-described embodiment(s) of the invention without departing substantially from the spirit and principles of the invention. All such modifications and variations are intended to be included herein within the scope of this disclosure and the present invention and protected by the following claims.

Claims (23)

1. A piezoelectric resonator, including:

a resonating member having a bi-directionally adjustable resonance frequency, said resonating member including:

a semiconductor material of a semiconductor-on-insulator wafer, the semiconductor-on-insulator wafer including an oxide layer adjacent to the semiconductor material and a handle layer adjacent to the oxide layer, the oxide layer disposed between the handle layer and the semiconductor material;

an electrode;

a piezoelectric material disposed between the semiconductor material and the electrode; and

a capacitor created by the semiconductor material and the handle layer separated by an air gap formed out of the oxide layer, wherein the capacitor is configured to receive a direct current voltage that adjusts the resonance frequency of the resonating member.

2. The piezoelectric resonator ofclaim 1, further including, in response to an excitation force applied to the resonating member, a quality factor for a beam configuration that ranges between approximately 2400-6200 for resonance frequencies ranging between approximately 1.72 megahertz-6.7 mega-hertz.

3. The piezoelectric resonator ofclaim 1, further including, in response to an excitation force applied to the resonating member, a quality factor for a beam configuration that ranges between approximately 3000-6200 for resonance frequencies ranging between approximately 1.72 megahertz-4.87 mega-hertz.

4. The piezoelectric resonator ofclaim 1, further including, in response to an excitation force applied to the resonating member, a quality factor for a beam configuration that ranges between approximately 5300-6200 for resonance frequencies ranging between approximately 1.72 megahertz-3.29 mega-hertz.

5. The piezoelectric resonator ofclaim 1, further including, in response to an excitation force applied to the resonating member, a quality factor for a beam configuration that ranges between approximately 5400-6200 for resonance frequencies ranging between approximately 0.721 megahertz-1.72 mega-hertz.

6. The piezoelectric resonator ofclaim 1, further including, in response to an excitation force applied to the resonating member, a quality factor for a block configuration that ranges between approximately 5500-11,600 for resonance frequencies ranging between approximately 16.9 megahertz-195 mega-hertz.

7. The piezoelectric resonator ofclaim 1, further including, in response to an excitation force applied to the resonating member, a quality factor for a block configuration that ranges between approximately 4700-11,600 for resonance frequencies ranging between approximately 16.9 megahertz-195 mega-hertz.

8. The piezoelectric resonator ofclaim 1, further including, in response to an excitation force applied to the resonating member, a quality factor for a block configuration that ranges between approximately 4500-11,600 for resonance frequencies ranging between approximately 16.9 megahertz-195 mega-hertz.

9. The piezoelectric resonator ofclaim 1, wherein the semiconductor material, the electrode, and the piezoelectric material are configured in one of a beam configuration and a block configuration.

10. The piezoelectric resonator ofclaim 1, wherein the electrode includes one of a sense electrode and a drive electrode.

11. The piezoelectric resonator ofclaim 10, wherein the sense electrode and the drive electrode are separated by the piezoelectric material.

12. The piezoelectric resonator ofclaim 10, wherein the sense electrode and the drive electrode are separated by the surface of the semiconductor material.

13. The piezoelectric resonator ofclaim 1, wherein the thickness of the semiconductor material ranges between approximately 0.2-30 microns.

14. The piezoelectric resonator ofclaim 1, wherein the piezoelectric material includes one of zinc oxide, aluminum nitride, and lead zirconate titanate.

15. The piezoelectric resonator ofclaim 1, wherein the semiconductor material includes one of silicon, germanium, single crystal semiconductor material, polycrystalline semiconductor material, and amorphous semiconductor material.

16. The piezoelectric resonator ofclaim 1, further including an adhesion layer disposed between the piezoelectric material and the semiconductor material.

17. The piezoelectric resonator ofclaim 1, wherein the resonating member includes a resonance frequency resulting from at least one of in-plane and out-of-plane movement of the resonating member.

18. A communications device, including:

a receiver; and

a piezoelectric resonator disposed in the receiver, the piezoelectric resonator including:

a resonating member having a bi-directionally adjustable resonance frequency, said resonating member including:

a semiconductor material of a semiconductor-on-insulator wafer, the semiconductor-on-insulator wafer including an oxide layer adjacent to the semiconductor material and a handle layer adjacent to the oxide layer, the oxide layer disposed between the handle layer and the semiconductor material;

an electrode;

a piezoelectric material disposed between the semiconductor material and the electrode; and

a capacitor created by the semiconductor material and the handle layer separated by an air gap formed out of the oxide layer, wherein the capacitor is configured to receive a direct current voltage that adjusts the resonance frequency of the resonating member.

19. The communications device ofclaim 18, wherein the piezoelectric resonator is configured as at least one of a filter and a frequency reference device.

20. The communications device ofclaim 18, further including a transmitter.

21. The communications device ofclaim 20, wherein the transmitter includes a second piezoelectric resonator, wherein the second piezoelectric resonator is configured as at least one of a filter and a frequency reference device.

22. The piezoelectric resonator ofclaim 1, further including a capacitor created by a second electrode disposed adjacent to the piezoelectric resonator and separated by a gap, wherein the capacitor is configured to receive a direct current voltage to adjust the resonance frequency of the resonating member.

23. The piezoelectric resonator ofclaim 1, wherein the oxide layer is a thin film layer of a thickness ranging between and including 0.1-5 microns.

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